A096493 Number of distinct primes in continued fraction period of square root of n.

0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 3, 0, 1, 1, 2, 1, 1, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 0, 3, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0

Offset: 1

Author

Labos Elemer, Jun 29 2004

Keywords

• nonn

Examples

			n=127: the period={3,1,2,2,7,11,7,2,2,1,3,22},
distinct-primes={2,3,7,11}, so a[127]=4;
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A003285, A013646, A096491, A096492.

Programs

Mathematica

{te=Table[0, {m}], u=1}; Do[s=Count[PrimeQ[Union[Last[ContinuedFraction[n^(1/2)]]]], True]; te[[u]]=s;u=u+1, {n, 1, m}];te
dpcf[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],0,Count[Union[ ContinuedFraction[ s][[2]]],?PrimeQ]]]; Array[dpcf,110] (* _Harvey P. Dale, Mar 18 2016 *)